# Electrical and thermoelectric transport properties of two-dimensional fermionic systems with $k$-cubic spin-orbit coupling

## TL;DR

This paper analytically studies how $k$-cubic spin-orbit interaction influences electrical and thermoelectric transport in 2D fermionic systems, revealing suppressed scattering directions, adherence to Wiedemann-Franz law, and magnetic field signatures useful for measuring spin-orbit coupling.

## Contribution

It provides exact analytical expressions for transport properties considering $k$-cubic RSOC, including scattering suppression directions and magneto-oscillation patterns, advancing understanding of spin-orbit effects in 2D systems.

## Key findings

- Scattering is suppressed along specific directions due to $k$-cubic RSOC.
- Thermoelectric coefficients obey Wiedemann-Franz law at low temperatures.
- Beating patterns in SdH oscillations reveal spin-orbit coupling strength.

## Abstract

We investigate the effect of $k$-cubic spin-orbit interaction on electrical and thermoelectric transport properties of two-dimensional fermionic systems. We obtain exact analytical expressions of the inverse relaxation time (IRT) and the Drude conductivity for long-range Coulomb and short-range delta scattering potentials. The IRT reveals that the scattering is completely suppressed along the three directions $\theta^\prime = (2n+1)\pi/3 $ with $ n=1,2,3$. We also obtain analytical results of the thermopower and thermal conductivity at low temperature. The thermoelectric transport coefficients obey the Wiedemann-Franz law, even in the presence of $k$-cubic Rashba spin-orbit coupling (RSOC) at low temperature. In the presence of quantizing magnetic field, the signature of the RSOC is revealed through the appearance of the beating pattern in the Shubnikov-de Haas (SdH) oscillations of thermopower and thermal conductivity in low magnetic field regime. The empirical formulae for the SdH oscillation frequencies accurately describe the locations of the beating nodes. The beating pattern in magnetothermoelectric measurement can be used to extract the spin-orbit coupling constant.